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Title: Hydrodynamic limits under pressure
Author: Marchesani, Stefano
ISNI:       0000 0004 7652 4003
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2017
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We study the hydrodynamic limit for a one dimensional isothermal anharmonic finite chain in Lagrangian coordinates with hyperbolic space-time scaling. The temperature is kept constant by putting the chain in contact with a heath bath, realised via the addition of a stochastic momentum-preserving noise to the dynamics of the chain. The noise is designed to be large at the microscopic level, but vanishing in the hydrodynamic limit. Boundary conditions are also considered: one end of the chain is kept fixed, while a time-variable tension is applied to the other end. We show that the microscopic deformation and momentum converge (in an appropriate sense) to solutions of a system of hyperbolic conservation laws (isothermal Euler equations in Lagrangian coordinates) with boundary conditions. Since these solutions may develop shocks in a finite time, they are obtained in a weak sense. This is done by adapting the theory of compensated compactness to a stochastic setting. Finally, the external tension allows us to define thermodynamic transformations between equilibrium states. We use this to deduce the first and the second principle of Thermodynamics for our model.
Supervisor: Chen, Gui-Qiang Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available